Open Question #1

Something is a lot lighter than your drinking cup. What might it be?

Sample answers:
A small box of raisins

OR My pencil

Open Question #2

Suppose □ + 4 = △ – 8.
What might the values of □ and △ be?

Sample answers:
They might be 8 and 20 since 8 + 4 = 20 – 8.

OR They might be 6 and 18 since 6 + 4 = 18 – 8.

Open Question #3

Two times are close to 2 hours apart but not exactly. Fill in the blanks to show what the times might be.
                  :         a.m. and         :         p.m.

Sample answer:
10:55 a.m. and 12:45 p.m.

Open Question #4

Fill in the blanks below with numbers from 1 to 9. You can use each digit only once. Then solve each equation.

              × 8 = a               4 × b =                       

          6      ÷ c =                   5 ÷ d =          

               2 ÷ e =    

Sample answers:
2 × 8 = a, so a = 16
4 × a = 3 6 , so a = 9
6 4 ÷ a = 8 , so a = 8
1 5 ÷ a = 5 , so a = 3
7 2 ÷ a = 9 , so a = 8

OR 9 × 8 = a, so a = 72
4 × a = 7 6 , so a = 19
6 8 ÷ a = 2 , so a = 34
1 5 ÷ a = 5 , so a = 3
3 2 ÷ a = 4 , so a = 8

Open Question #5

Two angles in a triangle are in the ratio 2 : 5. What might the three angles be?

Sample answer:
If one angle is 20° and another is 50°, the third is 110°.
OR
If one angle is 32° and another is 80°, the last is 68°.

Open Question #6

The solution to an equation involving subtraction and division is 10 more than the solution to an equation involving addition and multiplication.
What could the two equations be?

Sample answer:
I started with the first equation and chose some numbers that are easy to subtract and divide:
(85 – 5) ÷ a = 5
80 ÷ a = 5
80 = 5a
16 = a

Now that I have my first equation, I know that my second equation has to have a solution that is 10 less, or 6:
2x + 8 = 20
2x = 20 – 8
2x = 12
x = 6

So, the first equation could be (85 – 5) ÷ a = 5, and the second equation could be 2x + 8 = 20.